Course Co-ordinated by IIT Kanpur
 Coordinators IIT Kanpur

Untitled Document

Basic facts of maxima & minima & convex optimization.
Important classes of convex optimization problems.
Convex sets & convex functions
Differentiable convex functions
Projection on a convex set and normal cone
Sub differential of a convex.
Karush-kuhn-Tucker Conditions
Lagrangian duality and examples.
Strong duality & consequences.
Linear programming, basics & examples.
Basic results and the fundamental theorems of linear programming
Simplex method
Introduction to interior point methods
Short step path following method .
Semi definite programming
Approximate solutions.

 Lecture/Module Topics 1 Basics of Convex Optimization 2 Basic facts of Convex Optimization 3 Basic properties of convex sets 4 Introduction to Polyhedral sets 5 Separation theorems for convex sets 6 Theorems of the alternative 7 Continuity and differentiability properties of convex functions 8 Non differentiable convex functions 9 Calculus of Sub differentials 10 Rockafeller-Pshenichny optimality condition 11 Properties of normals & projections 12 Computing the normal cone of inequality constraints. 13 Tangent cone 14 Fenchel conjugate continues. 15 Minimization of a convex function with convex inequality constraints is considered 16 Lagrangian Duality 17 Duality in connection with Linear Programming 18 Strong duality for convex problem 19 Pleasures of Linear Programming 20 Direction of descent 21 Extreme points of Linear Programming 22 Polyhedral sets & cones 23 Foundation of simplex methods 24 Fundamental theorem of Linear programming 25 Simplex methods 26 Simplex methods continued 27 Interior point methods 28 Interior point methods continued 29 Log barrier function 30 Primal-dual framework 31 Overview of interior point algorithm 32 Short step algorithm 33 Predictor-corrector method 34 Semi-definite programming 35 Saddle point type conditions for SDP. 36 Approximate solutions 37 Descent direction for non-smooth functions 38 Minimization of difference convex functions 39 Minimization of difference convex functions continues. 40 Concluding lecture.

Knowledge in Linear Algebra & Real Analysis

1. Stories about Maxima & Minima By V.M. Tikhomirov Pub: American Mathematical Society.
2. Convex Optimization By S. Boyd Pub: Cambridge University Press
3. Convex Analysis and Minimization Algorithms By J.B.Hiriat-Uruty& Lemarechal Pub: Springer
4. Convex Analysis By R.T.Rockafellar, Pub: Princeton

Stephen Byod lectures on Convex Optimization